Toupin's version of the Saint-Venant's principle in linear elasticity is generalized to the case of linear elastic porous materials. That is, it is shown that, for a straight prismatic bar made of a linear elastic material with voids and loaded by a self-equilibrated system of forces, at one end only, the internal energy stored in the portion of the bar which is beyond a distance s from the loa...

We consider a homogeneous space X = (X, d,m) of dimension ν ≥ 1 and a local regular Dirichlet form in L2 (X,m) . We prove that if a Poincaré inequality of exponent 1 ≤ p < ν holds on every pseudo-ball B (x,R) of X, with local characteristic constant c0 (x) and c1 (r), then a Green’s function estimate from above and below is obtained. A Saint-Venant-like principle is recovered in terms of the En...

Toupin's version of the Saint-Venant principle in linear elasticity is generalized to the case of linear elasticity with mierostructure. That is, it is shown that, for a straight prismatic bar made of an isotropic linear elastic material with rnicrostructure and loaded by a self-equilibrated force system at one end only, the strain energy stored in the portion of the bar which is beyond a dista...

We consider a cylindrical three-dimensional body, made of a Saint Venant-Kirchhoff material, and we let its thickness go to zero. For a specific order of magnitude for the applied loads and under appropriate restrictions on the set of admissible deformations, we show that the almost-minimizers of the total energy converge toward deformations that minimize the nonlinear bending energy obtained b...

Explicit boundary dissipative conditions are given for the exponential stability in L2-norm of onedimensional linear hyperbolic systems of balance laws ∂tξ + Λ∂xξ −Mξ = 0 over a finite interval, when the matrix M is marginally diagonally stable. The result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised Saint–Venant–Exner equation...

Sediment of different size are transported in rivers under the action of flow. The first and still most popular sediment continuity model able to deal with mixed sediment is the so-called active layer model proposed by Hirano (1971, 1972). In this paper, we consider the one-dimensional hydromorphodynamic model given by the Saint-Venant equations for free-surface flow coupled with the active lay...

We study the exponential stability in H 2 norm of nonlinear Saint-Venant (or shallow water) equations with arbitrary friction and slope using a single proportional-integral (PI) control at one end channel. Using good but simple Lyapunov function we find explicit condition on gain PI to ensure any steady-states. This is independent slope, coefficient, length river, inflow disturbance and, more s...

An overview is given of finite volume central schemes for the numerical solution of systems of conservation and balance laws. Well balanced central schemes on staggered grid for the Saint-Venant model or river flow are considered. A scheme which is well balanced for channels with variable cross section is introduced. Finally, a scheme which preserves non static equilibria is introduced, and som...